Monthly Archives: October 2007

I and a couple of friends were engaged in what was intended to be nothing more than a chitchat when things stirred up. We were wondering away at some imminent wed locks when we digressed a shade onto the contentious dowry issue. We were ridiculing the outrageous amounts that some of our batch mates would receive, should they choose to accept. The last part of the previous statement is of interest here: Whether the dowry will be turned down or not, if offered. I always thought (naively, in hindsight) that all the people, as well-educated as I am, would not even contemplate accepting it. However, I was a bit taken aback when, one of my friends, the one who had forked this topic into discussion, said while he would never “ask for” any kinda dowry, he would have no issues in accepting it if the gal’s family made an offer!

One might be tempted into arguing that if I am given a ‘gift’, am I not well within my rights to accept it. The problem with this line of thought is that it looks at the receipt of dowry in isolation, devoid of the gender context. Gifts are acceptable when they are mutual. Dowry is always given by the bride’s family, never reciprocated. Moreover, though it is a voluntary act in cases like the aforementioned one, more often than not, there is some sort of coercion involved. Even in voluntary cases, there’s an issue. The moment it is known that you were open to dowry or you accepted it, many girl parents could find themselves revisiting their stance on the matter. Similarly, after seeing their peers take dowry, boy parents might also be emboldened to cash in on some cheap cash. What at first glance seems like a harmless acceptance of ‘gifts’ actually helps perpetuate a vicious cycle that forces women to lead the lives of second-class citizens.

Problem 1: Given a set of 2D points, find an efficient way of computing the least area rectangle that encloses them.

One (probably good) way of approaching this to stamp down on the data size by first showing that the least-area enclosing rectangle of these points is the same as that of the convex hull of the points (For now, I have taken this for granted) and working only on the hull points thereafter.

But, this is just data reduction. How do we use these points to compute the rectangle? The approach I have successfully implemented is not as efficient as I would like it to be. I based my thing on parameterizing the min area rectangle by just the orientation parameter. This is because once the orientation is frozen, once can easily and uniquely determine the min area rectangle by computing minx, maxx, miny, maxy along that and its perpendicular direction. So, it boiled down to optimization in the angle space. Currently, I am using a brute force method but one can study the objective function and better the convergence. However, I have an inkling that there is a non-iterative, closed-form solution to this. To discuss about and arrive at that elegant solution, actually, is the motive of this post.

The second problem is similar but a little more complex. I will post my solution (again, suboptimal) once (and if) there is some interaction about the first one. I will leave you with the problem statement, nevertheless.

Problem 2: Given a set of 2D points, find, efficiently, the maximum area rectangle that is enclosed within their convex hull.